Register allocation for software pipelined multi-dimensional loops

摘要

Software pipelining of a multi-dimensional loop is an important optimization that overlaps the execution of successive outermost loop iterations to explore instruction-level parallelism from the entire n-dimensional iteration space. This paper investigates register allocation for software pipelined multi-dimensional loops.For single loop software pipelining, the lifetime instances of a loop variant in successive iterations of the loop form a repetitive pattern. An effective register allocation method is to represent the pattern as a vector of lifetimes (or a vector lifetime using Rau's terminology) and map it to rotating registers. Unfortunately, the software pipelined schedule of a multi-dimensional loop is considerably more complex, and so are the vector lifetimes in it.In this paper, we develop a way to normalize and represent vector lifetimes in multi-dimensional loop software pipelining, which capture their complexity, while exposing their regularity that enables us to develop a simple, yet powerful solution. Our algorithm is based on the development of a metric, called distance, that quantitatively determines the degree of potential overlapping (conflicts) between two vector lifetimes. We show how to calculate and use the distance, conservatively or aggressively, to guide the register allocation of the vector lifetimes under a bin-packing algorithm framework. The classical register allocation for software pipelined single loops is subsumed by our method as a special case.The method has been implemented in the ORC compiler and produced code for the Itanium architecture. We report the effectiveness of our method on 134 loop nests with 348 loop levels. Several strategies for register allocation are compared and analyzed.